Rename parser dir to parse (#3178)

Continuing with #3070. Just a dir and file rename (mostly removing
prefixes, although for parse_tree_fuzzer and parse_tree_file_test I'm
dropping "tree" instead of "parse"). Everything in the parse dir should
be marked as a move.

toolchain/parse/handle_namespace.cpp

@@ -0,0 +1,39 @@
+// Part of the Carbon Language project, under the Apache License v2.0 with LLVM
+// Exceptions. See /LICENSE for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+
+#include "toolchain/parse/context.h"
+
+namespace Carbon::Parse {
+
+auto HandleNamespace(Context& context) -> void {
+  auto state = context.PopState();
+
+  context.AddLeafNode(NodeKind::NamespaceStart, context.Consume());
+
+  state.state = State::NamespaceFinish;
+  context.PushState(state);
+
+  context.PushState(State::DeclarationNameAndParamsAsNone, state.token);
+}
+
+auto HandleNamespaceFinish(Context& context) -> void {
+  auto state = context.PopState();
+
+  if (state.has_error) {
+    context.RecoverFromDeclarationError(state, NodeKind::Namespace,
+                                        /*skip_past_likely_end=*/true);
+    return;
+  }
+
+  if (auto semi = context.ConsumeIf(Lex::TokenKind::Semi)) {
+    context.AddNode(NodeKind::Namespace, *semi, state.subtree_start,
+                    state.has_error);
+  } else {
+    context.EmitExpectedDeclarationSemi(Lex::TokenKind::Namespace);
+    context.RecoverFromDeclarationError(state, NodeKind::Namespace,
+                                        /*skip_past_likely_end=*/true);
+  }
+}
+
+}  // namespace Carbon::Parse